# Fast Integral solver : A Ti-84 Basic program

## Explanation of the fast integral solver

The standard integral solver in the math menu of the Ti-84 plus calculator is based on the Gauss-Kronrod method and is optimized for integration of determined x-values.There are cases where you are not only interested in one specific value of the integral, but in the behavior of the function over its course. In the example below, we do not want to integrate from 0 to a fixed upper limit of π/2, but to a variable X that varies from 0 to π/2. The result will give you the graphical solution of an integral. Although the result is not a formula (which you get with a CAS solver) it gives you a good insight into the course of the function and can be used to check your analytical result (which is sin(x) for this problem).

Although this is a good alternative if you have no CAS solver, the processing time is very long (up to minutes for complicated functions). Therefore, a program with a much faster integral solver has been, and the processing time is a few seconds. The program is named FASTINT2. The accuracy depends on the number of steps which you can choose. In the results below, a comparison is made between the standard Ti-solver and the program FASTINT.It demonstrates that the FASTINT program can be more than 30 times faster than the standard solver while still maintaining a high degree of accuracy. The first example is a simple function for the input: the integral of cos(x).

The second example is a more complicated integral which, in my opinion, cannot be solved analytically. Using the standard integral method of the Ti-84 takes more than 4 minutes (240 seconds).The FASTINT2 solver only needs 7 seconds to solve the problem with a good degree of accuracy.

A new version is available where also Xmin has to be defined.

Download the program FASTINT3.8xp :